Magnetic Resonance Elastography (MRE) is an emerging imaging modality which seeks to recover high resolution maps of tissue mechanical properties. While the technique has been advanced considerably over the last several years and a number of promising clinical applications are now being investigated, almost all of the results produced to date have been based on the assumption that tissue is linearly elastic. However, it is generally accepted that many tissues do not respond as an isotropic linearly-elastic medium but rather exhibit more complex mechanical behaviors. Specifically, they can be more accurately represented by viscoelastic, anisotropic and nonlinear mechanical properties. As a result it seems critical to extend MRE methodology to account for these more complete and accurate mechanical property characterizations if the technique is to realize its full potential as an aid to diagnostic decision-making. The overall goal of the proposed project is to develop, validate and evaluate MRE methods for imaging the mechanical property parameters associated with conventional model descriptions of tissue as either a viscoelastic, an anisotropic or a nonlinear medium in terms of its mechanical response to the stimulus applied during MRE procedures. The specific aims of the project are to (1) Develop the MR data acquisition techniques required to observe these complex mechanical effects in phantoms that possess the targeted behaviors, (2) Develop the algorithms for converting the MR displacement data into mechanical property estimates which characterize the phantom materials used, and (3) Validate these developments through a series of simulation and phantom experiments which (a) determine the accuracy, stability and uniqueness of the mechanical property estimation process, (b) optimize the trade-off between model complexity which accurately characterizes the motion (and mechanical properties) and model efficiency/stability which provides robustness when algorithms are applied to in vivo data, and (c) identify the magnitude of the inaccuracies in shear modulus estimation incurred by assumptions of linear elasticity when the medium exhibits more complex mechanical properties.